Monthly Archives: November 2008

Matt Springer, of Texas A&M, via his blog Built On Facts is sending me large numbers of visitors so I thought I would share a small part of the history of Texas, and the Texas navy.

Texas was a part of Mexico when the colony of Spain obtained independence as a result of the Mexican War of Independence, 1810-1821. There followed a brief empire under Agustín de Iturbide followed by the first Mexican Republic in 1824 with Guadalupe Victoria (an assumed name) as President. The election to succeed Guadalupe Victoria was one by the founder of the Partido Moderador (Moderate Party), Manuel Gómez Pedraza, however, before he could take office, the now infamous Antonio López de Santa Anna forced him out and annulled the election. Antonio López de Santa Anna installed the first arguably African-American president of a major North American country, Vicente Guerrero, into power. One of Vicente Guerrero’s most important acts of his brief (1 April 1829 – 17 December 1829) term in power was to ban slavery and emancipate all slaves. The Presidency of Vicente Guerrero ended when his Vice President, Anastasio Bustamante lead a coup against him (and had him executed). More unrest followed, but many must have thought that Mexico was slowly becoming a democracy.

Liberal changes may be good (especially applied to conditions of the early 19th century), but Valentín Gómez Farías changed things too much and too fast for the Catholic and military parts of Mexico which revolted against him. The resulting conflict saw Antonio López de Santa Anna in power as President with the followers of Valentín Gómez Farías forced to hide or leave (mostly to the United States). Enough with democracy; Antonio López de Santa Anna reformed Mexico into a Catholic dictatorship in 1836 and tore up the Constitution of 1824. The new Constitution of 1835 eliminated the loose confederation of states and created a powerful federal government.Continue reading →

I’ve just submitted a paper, Density Matrices and the Weak Quantum Numbers to Foundations of Physics. There are things about the paper that I didn’t include, things that I didn’t think were appropriate to a journal submission and I thought I’d talk about them here, and explain what the paper is talking about to a more general (but still math/physics) audience.

The paper is on the subject of the weak quantum numbers of the left and right handed elementary fermions and anti-fermions. Ignoring color and generation, there are 16 of these quantum objects. I provide a method of defining these quantum numbers by an idempotency equation, that is, by solving an equation of the form . Since pure density matrices satisfy this equation, the calculation is a density matrix calculation based on the permutation group on 3 elements.

The usual method of elementary particles is to assume that a symmetry relates the quantum states. In this calculation, the quantum states themselves are assumed to be composed of group elements of the symmtry. This can be done in density matrix formalism because density matrices can operate on themselves. Also of interest are what happens when different density matrices operate on each other. Particularly when the density matrices are chosen from the basis states of a complete set of mutually unbiased bases. But that’s another paper (mostly written).

A “Centauro” is an event with an excess of hadrons relative to electromagnetics. The opposite event, the “anti-Centauro” is an excess of electromagnetics (muons) over hadrons. (For non particle people, I’ll put an explanation of what “electromagnetics” has to do with “muons” below the fold.)

For the particle people, it’s best to just quote the paper. This is section “3.3 JACEE Experiment”, around page 63:

The Japanese-American Cooperative Emulsion Chamber Experiment, JACEE, has flown emulsion chambers with baloons near the top of the atmosphere. Despite of a small area and short time of exposure, as compared to Chacaltaya/Pamir Experiment, a few events of anomalous γ/charged ratio have been observed by JACEE Collaboration. However, these events differ in some essential points from classical Centauros. The anomalies were noticed at incident energies lower than that estimated for “classical” Centauros and unusual γ/charged ratios were observed only in the limited (η − φ) phase space region. Besides that, an excess of photons (anti–Centauro), in contrary to the hadron excess observed in Centauros, was claimed. The examples are:

1.) 4L-II-27 event [74] of incident energy of 80 TeV, yielded 149 charged particles and 120 γ’s. Almost all γ–quanta were produced in a narrow jet in the extreme forward direction. The γ/charged ratio is 2.6 ± 1.1 in the region of pseudorapidity 5.5 ≤ η ≤ 7.5, what is a significant deviation from the expected ratio of ∼ 1. The analysis presented in [74] showed an anomaly at the 5-10% level among 41 studied events with E0 ≥ 40 TeV.

2.) The event, with ΣE = 15.4 TeV, described in [75, 76] was initiated by a singly charged primary. The collision occurred within the detector. Almost all leading particles were γ–quanta. Photons appear to cluster into two groups. The leading cluster consisted of about 32 γ’s with hpT i ≃ 200 MeV and only one accompanying charged particle. A possibly distinct cluster had three times as many photons as charged hadrons (about 54 photons versus 17 charged). This event is one out of a sample of about 70.

3.) The event presented in [77] is a peripheral collision of Fe nucleus (E ≃ 9 TeV/nucleon) in emulsion. There were found 27 γ–quanta with η ≤ 6. As they came from pair conversions at only 0.8 radiation lengths, one can expect that the total number of photons was about 50. At the same time, only 6 charged particles (out of 21 charged tracks detected in the whole angular region) falled in the same kinematical range.

In all these events there was observed a tendency to a group emission of mesons. Such groups, having similar directions and momenta, could be signs of a formation and a subsequent decay of the chiral condensates. It should be mentioned, however, that these events were found in emulsion by scanning for the leading photon showers, so there was a “trigger bias” in favour of a large neutral fraction. It would be interesting to hear something about anti-Centauros from the mountain-top emulsion chambers. Here, there is, however, even much more stronger “trigger bias” in favour of gamma families, and thus the interpretation of data, from this point of view, is a complicated exercise. It is rather difficult to identify anti–Centauros unambigously, with exception of unusual and rare events in which the interaction vertex is close to the top and clearly resolved in the chamber.